The rocket lifted off at 3:44 a.m. ET from Cape Canaveral Air Force Station in Florida carrying an unmanned version of the private firm's Dragon space capsule.

This morning's successful launch comes after numerous delays and a launch abort on Saturday, which was triggered by an anomalous pressure reading in the combustion chamber of one of the rocket's nine launch engines.

Today, though, "Falcon flew perfectly!!," SpaceX CEO Elon Musk wrote on Twitter moments after the launch. "Feels like a giant weight just came off my back :)."

At a press conference held after the launch, Musk said that "every bit of adrenalin in my body released at that point," and that the elation he felt was like "winning the Super Bowl."

"I would really count today as a success no matter what happens for the rest of the mission."

"It's a great day for America. It's a great day for the world," Bolden told reporters afterward.

"There were people who thought that [NASA] had gone away [with the retirement of the space shuttles]. But today says, No, we're not gone away at all. We've got the SpaceX-NASA team, and they came through this morning with flying colors."

SpaceX CEO Gwen Shotwell also confirmed at the press conference that, as part of its mission, Falcon 9 carried cremated remains, which were released into orbit.

The ashes were flown as part of a deal with Celestis, a company that specializes in "memorial spaceflights."

Today's payload reportedly contained the remains of more than 300 people, including actor James Doohan—who played Scotty on the original Star Trek television series—and Mercury program astronaut Gordon Cooper. Shotwell didn't comment on the identities of the ashes.

Dragon Now in Flight

The gumdrop-shaped Dragon capsule—stuffed with cargo for the ISS crew—separated from the rocket components approximately ten minutes after launch and deployed a pair of solar arrays.

"Dragon is now free-flying in orbit around the Earth," a SpaceX official said amid cheers during a live online broadcast of the launch.

Over the next several days, Dragon will undergo a gauntlet of test maneuvers and systems demonstrations before being allowed to berth with the space station on Friday.

William Gerstenmaier, associate administrator for NASA's Human Exploration Operations Directorate, said today that Dragon could pass the overall demonstration flight even if it fails one of the tests.

"We'll take a look at how the mission goes, and then we'll analyze what occurs, and if we think the failure is small enough, it can be easily corrected and we can go straight into commercial resupply," Gerstenmaier said.

"If it's something that we collectively think requires a lot of extra work and would actually benefit from another test flight, then we would go propose [another] test flight."

Dragon is scheduled to detach from the ISS and return to Earth next Thursday, landing in the Pacific Ocean off Southern California to be retreived by ship.

Launch to Be Historic Milestone

Robert Pearlman, editor of the space-history and artifacts website collectSPACE.com, called the Dragon test mission a potentially historic milestone for the future of spaceflight.

"It could set the stage for not just a series of cargo deliveries," he said, "but for American astronaut deliveries to the space station, as well as eventually establish a commercial spaceflight industry here in the United States outside of just satellite launches."

One of Dragon's most crucial tests will be to determine whether its piloting software can follow instructions from astronauts aboard the ISS in case they decide to abort the vehicle's approach to the space station.

"If Dragon is near the space station and something goes wrong, you want the astronauts to be able to say 'abort' and have the spacecraft leave without damaging anything," said SpaceX spokesperson Kirstin Brost Grantham.

If Dragon passes the abort test, a robotic arm attached to the ISS will snatch the capsule and bring it in for berthing. In the future, Dragon will be able to dock with the space station under its own power, Brost Grantham said.

Before it berths, collectSPACE.com's Pearlman added, Dragon will have to perform one last test.

"Upon final approach, when it comes within a distance that the [robotic] arm can reach it, it will have to demonstrate that it can actually stay there and be stable in orbit without causing trouble to the arm or the station or itself."

Dragon to Bring Back Experiments, Old Gloves

Because this mission is primarily a test demonstration, Dragon is not carrying any essential items to the space station or back to Earth.

For example, the launch manifest includes clothing for astronauts, extra food, and laptop batteries. The return payload will include hardware from completed space station experiments and old space suit gloves from past ISS inhabitants.

For now NASA can transport items to the space station using automated transfer vehicles operated by the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA).

But these transporters are designed for one-way trips only and burn up on reentry, making return cargo trips impossible.

The Russian Soyuz spacecraft—currently NASA's only way of transporting astronauts to the ISS—does have the ability to return to Earth, but "its primary function is to return humans, not payload," Pearlman said.

Manned Private Flights by 2015?

SpaceX's Brost Grantham added that while the company is confident in its vehicles and software, success is not guaranteed.

"Every step of this mission is incredibly complicated," she said. "Whatever happens, we're going to learn more from this mission. We know that, because it's a test flight, it's inherently risky ... so it's entirely possible we're unable to accomplish all of our objectives, but we will learn from that."

SpaceX predicts that the first manned Dragon flights could occur as early as 2015. But before that happens, the spacecraft will need to be outfitted with more environmental controls and crew accommodations, something the company is already working on, according to Brost Grantham.

"A few months ago we had NASA astronauts come out and do a test of the accommodations to make sure it meets their needs," she said.

SpaceX will also have to demonstrate a successful launch-abort system for Dragon—using upgraded thrusters dubbed "SuperDracos"—before NASA will allow it to be used as a crew-transport vehicle.

"If there's an emergency, there will be these superthrusters on the side of the spacecraft that turn on and will immediately carry the astronauts a safe distance from the rocket," Brost Grantham said.

Musk said today that work on SuperDraco is proceeding smoothly. "We've had a number of successful firings of that thruster, and we'll be integrating it into a ... propulsion module hopefully later this year."

So far, NASA and SpaceX appear to have a good working relationship, collectSPACE.com's Pearlman added.

"I think NASA and SpaceX are working just as well as NASA and Boeing, NASA and Lockheed, and NASA and any of its other suppliers."